{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tvd(p, q):\n",
    "    return 1/2*np.sum(np.abs(p - q))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the pickle file with proper file handling\n",
    "# Input: path to the pickle file\n",
    "# Output: mitigated_res object loaded from the pickle file\n",
    "with open(\"mitigated_res.pkl\", \"rb\") as f:\n",
    "    mitigated_res = pickle.load(f)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {},
   "outputs": [],
   "source": [
    "h_res = []\n",
    "ry1_res = []\n",
    "ry2_res = []\n",
    "\n",
    "for k, v in mitigated_res.items():\n",
    "    if 'h' in k:\n",
    "        h_res.append(v)\n",
    "    elif 'ry1' in k:\n",
    "        ry1_res.append(v)\n",
    "    elif 'ry2' in k:\n",
    "        ry2_res.append(v)\n",
    "\n",
    "h_res.append(np.array([0.5, 0.5]))\n",
    "ry1_res.append(np.array([0.9, 0.1]))\n",
    "ry2_res.append(np.array([0.1, 0.9]))\n",
    "               "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rcParams\n",
    "import numpy as np\n",
    "\n",
    "# Set up the plotting style for publication-quality figures\n",
    "# Input: None\n",
    "# Output: Configured matplotlib environment with appropriate styling\n",
    "plt.style.use('default')\n",
    "rcParams['font.family'] = 'sans-serif'\n",
    "rcParams['font.sans-serif'] = ['Arial']\n",
    "rcParams['font.size'] = 10\n",
    "rcParams['axes.linewidth'] = 1\n",
    "rcParams['axes.labelsize'] = 12\n",
    "rcParams['xtick.labelsize'] = 10\n",
    "rcParams['ytick.labelsize'] = 10\n",
    "rcParams['legend.fontsize'] = 10\n",
    "rcParams['figure.figsize'] = [12, 8]\n",
    "\n",
    "# Calculate TVD for each result in h_res compared to the ideal distribution\n",
    "# Input: h_res - list of probability distributions\n",
    "# Output: tvd_values - list of TVD values for each distribution\n",
    "ideal_dist = h_res[-1]  # Ideal distribution for H gate\n",
    "tvd_values = [tvd(dist, ideal_dist) for dist in h_res[:-1]]\n",
    "\n",
    "# Create a bar plot to visualize TVD values with grouped bars\n",
    "# Input: tvd_values - list of TVD values\n",
    "# Output: matplotlib figure showing TVD comparison with grouped bars\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Define the number of experiment groups\n",
    "num_experiments = len(tvd_values) // 2\n",
    "bar_width = 0.35\n",
    "index = np.arange(num_experiments)\n",
    "\n",
    "# Organize data for grouped bars (method1 and method2 for each experiment)\n",
    "method1_data = tvd_values[::2]  # Every even index (0, 2, 4...)\n",
    "method2_data = tvd_values[1::2]  # Every odd index (1, 3, 5...)\n",
    "\n",
    "# Plot bars for each method side by side\n",
    "bars1 = ax.bar(index - bar_width/2, method2_data, bar_width, \n",
    "               color='#2878B5', alpha=0.8, edgecolor='black', \n",
    "               linewidth=1, label='No matrix')\n",
    "bars2 = ax.bar(index + bar_width/2, method1_data, bar_width, \n",
    "               color='#FF7F0E', alpha=0.8, edgecolor='black', \n",
    "               linewidth=1, label='Matrix inversion')\n",
    "\n",
    "# Add a horizontal line at TVD=0 to indicate perfect fidelity\n",
    "ax.axhline(y=0, color='red', linestyle='--', alpha=0.7, linewidth=1)\n",
    "\n",
    "# Customize the plot\n",
    "ax.set_xlabel('Experiment Number', fontweight='bold')\n",
    "ax.set_ylabel('Total Variation Distance (TVD)', fontweight='bold')\n",
    "ax.set_title('TVD after Matrix Inversion(EXP-1)', fontweight='bold')\n",
    "ax.set_xticks(index)\n",
    "ax.set_xticklabels([\"Physical qubit 1\", \"Physical qubit 2\", \n",
    "                    \"Symmetric encoding\", \"Symmetric encoding\\nafter adding noise\"])\n",
    "ax.legend()\n",
    "\n",
    "# Add value labels on top of each bar\n",
    "def add_labels(bars):\n",
    "    for bar in bars:\n",
    "        height = bar.get_height()\n",
    "        ax.text(bar.get_x() + bar.get_width()/2., height + 0.0001,\n",
    "                f'{height:.5f}', ha='center', va='bottom', fontsize=9)\n",
    "\n",
    "add_labels(bars1)\n",
    "add_labels(bars2)\n",
    "\n",
    "# Add grid lines for better readability\n",
    "ax.grid(True, linestyle='--', alpha=0.7, axis='y')\n",
    "\n",
    "# Ensure proper layout\n",
    "plt.tight_layout()\n",
    "\n",
    "# Display the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rcParams\n",
    "import numpy as np\n",
    "\n",
    "# Set up the plotting style for publication-quality figures\n",
    "# Input: None\n",
    "# Output: Configured matplotlib environment with appropriate styling\n",
    "plt.style.use('default')\n",
    "rcParams['font.family'] = 'sans-serif'\n",
    "rcParams['font.sans-serif'] = ['Arial']\n",
    "rcParams['font.size'] = 10\n",
    "rcParams['axes.linewidth'] = 1\n",
    "rcParams['axes.labelsize'] = 12\n",
    "rcParams['xtick.labelsize'] = 10\n",
    "rcParams['ytick.labelsize'] = 10\n",
    "rcParams['legend.fontsize'] = 10\n",
    "rcParams['figure.figsize'] = [12, 8]\n",
    "\n",
    "# Calculate TVD for each result in h_res compared to the ideal distribution\n",
    "# Input: h_res - list of probability distributions\n",
    "# Output: tvd_values - list of TVD values for each distribution\n",
    "ideal_dist = ry1_res[-1]  # Ideal distribution for H gate\n",
    "tvd_values = [tvd(dist, ideal_dist) for dist in ry1_res[:-1]]\n",
    "\n",
    "# Create a bar plot to visualize TVD values with grouped bars\n",
    "# Input: tvd_values - list of TVD values\n",
    "# Output: matplotlib figure showing TVD comparison with grouped bars\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Define the number of experiment groups\n",
    "num_experiments = len(tvd_values) // 2\n",
    "bar_width = 0.35\n",
    "index = np.arange(num_experiments)\n",
    "\n",
    "# Organize data for grouped bars (method1 and method2 for each experiment)\n",
    "method1_data = tvd_values[::2]  # Every even index (0, 2, 4...)\n",
    "method2_data = tvd_values[1::2]  # Every odd index (1, 3, 5...)\n",
    "\n",
    "# Plot bars for each method side by side\n",
    "bars1 = ax.bar(index - bar_width/2, method2_data, bar_width, \n",
    "               color='#2878B5', alpha=0.8, edgecolor='black', \n",
    "               linewidth=1, label='No matrix')\n",
    "bars2 = ax.bar(index + bar_width/2, method1_data, bar_width, \n",
    "               color='#FF7F0E', alpha=0.8, edgecolor='black', \n",
    "               linewidth=1, label='Matrix inversion')\n",
    "\n",
    "# Add a horizontal line at TVD=0 to indicate perfect fidelity\n",
    "ax.axhline(y=0, color='red', linestyle='--', alpha=0.7, linewidth=1)\n",
    "\n",
    "# Customize the plot\n",
    "ax.set_xlabel('Experiment Number', fontweight='bold')\n",
    "ax.set_ylabel('Total Variation Distance (TVD)', fontweight='bold')\n",
    "ax.set_title('TVD after Matrix Inversion(EXP-2)', fontweight='bold')\n",
    "ax.set_xticks(index)\n",
    "ax.set_xticklabels([\"Physical qubit 1\", \"Physical qubit 2\", \n",
    "                    \"Symmetric encoding\", \"Symmetric encoding\\nafter adding noise\"])\n",
    "ax.legend()\n",
    "\n",
    "# Add value labels on top of each bar\n",
    "def add_labels(bars):\n",
    "    for bar in bars:\n",
    "        height = bar.get_height()\n",
    "        ax.text(bar.get_x() + bar.get_width()/2., height + 0.0001,\n",
    "                f'{height:.5f}', ha='center', va='bottom', fontsize=9)\n",
    "\n",
    "add_labels(bars1)\n",
    "add_labels(bars2)\n",
    "\n",
    "# Add grid lines for better readability\n",
    "ax.grid(True, linestyle='--', alpha=0.7, axis='y')\n",
    "\n",
    "# Ensure proper layout\n",
    "plt.tight_layout()\n",
    "\n",
    "# Display the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rcParams\n",
    "import numpy as np\n",
    "\n",
    "# Set up the plotting style for publication-quality figures\n",
    "# Input: None\n",
    "# Output: Configured matplotlib environment with appropriate styling\n",
    "plt.style.use('default')\n",
    "rcParams['font.family'] = 'sans-serif'\n",
    "rcParams['font.sans-serif'] = ['Arial']\n",
    "rcParams['font.size'] = 10\n",
    "rcParams['axes.linewidth'] = 1\n",
    "rcParams['axes.labelsize'] = 12\n",
    "rcParams['xtick.labelsize'] = 10\n",
    "rcParams['ytick.labelsize'] = 10\n",
    "rcParams['legend.fontsize'] = 10\n",
    "rcParams['figure.figsize'] = [12, 8]\n",
    "\n",
    "# Calculate TVD for each result in h_res compared to the ideal distribution\n",
    "# Input: h_res - list of probability distributions\n",
    "# Output: tvd_values - list of TVD values for each distribution\n",
    "ideal_dist = ry2_res[-1]  # Ideal distribution for H gate\n",
    "tvd_values = [tvd(dist, ideal_dist) for dist in ry2_res[:-1]]\n",
    "\n",
    "# Create a bar plot to visualize TVD values with grouped bars\n",
    "# Input: tvd_values - list of TVD values\n",
    "# Output: matplotlib figure showing TVD comparison with grouped bars\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Define the number of experiment groups\n",
    "num_experiments = len(tvd_values) // 2\n",
    "bar_width = 0.35\n",
    "index = np.arange(num_experiments)\n",
    "\n",
    "# Organize data for grouped bars (method1 and method2 for each experiment)\n",
    "method1_data = tvd_values[::2]  # Every even index (0, 2, 4...)\n",
    "method2_data = tvd_values[1::2]  # Every odd index (1, 3, 5...)\n",
    "\n",
    "# Plot bars for each method side by side\n",
    "bars1 = ax.bar(index - bar_width/2, method2_data, bar_width, \n",
    "               color='#2878B5', alpha=0.8, edgecolor='black', \n",
    "               linewidth=1, label='No matrix')\n",
    "bars2 = ax.bar(index + bar_width/2, method1_data, bar_width, \n",
    "               color='#FF7F0E', alpha=0.8, edgecolor='black', \n",
    "               linewidth=1, label='Matrix inversion')\n",
    "\n",
    "# Add a horizontal line at TVD=0 to indicate perfect fidelity\n",
    "ax.axhline(y=0, color='red', linestyle='--', alpha=0.7, linewidth=1)\n",
    "\n",
    "# Customize the plot\n",
    "ax.set_xlabel('Experiment Number', fontweight='bold')\n",
    "ax.set_ylabel('Total Variation Distance (TVD)', fontweight='bold')\n",
    "ax.set_title('TVD after Matrix Inversion(EXP-3)', fontweight='bold')\n",
    "ax.set_xticks(index)\n",
    "ax.set_xticklabels([\"Physical qubit 1\", \"Physical qubit 2\", \n",
    "                    \"Symmetric encoding\", \"Symmetric encoding\\nafter adding noise\"])\n",
    "ax.legend()\n",
    "\n",
    "# Add value labels on top of each bar\n",
    "def add_labels(bars):\n",
    "    for bar in bars:\n",
    "        height = bar.get_height()\n",
    "        ax.text(bar.get_x() + bar.get_width()/2., height + 0.0001,\n",
    "                f'{height:.5f}', ha='center', va='bottom', fontsize=9)\n",
    "\n",
    "add_labels(bars1)\n",
    "add_labels(bars2)\n",
    "\n",
    "# Add grid lines for better readability\n",
    "ax.grid(True, linestyle='--', alpha=0.7, axis='y')\n",
    "\n",
    "# Ensure proper layout\n",
    "plt.tight_layout()\n",
    "\n",
    "# Display the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Save experimental results to numpy files\n",
    "# The first argument to np.save should be the filename, not the array\n",
    "np.save(\"exp_h_res.npy\", np.array(h_res))\n",
    "np.save(\"exp_ry1_res.npy\", np.array(ry1_res))\n",
    "np.save(\"exp_ry2_res.npy\", np.array(ry2_res))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.21"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
